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Danylo Radchenko: Convolution identities for sums of even powers of divisors

Time: Wed 2024-02-28 13.00 - 13.50

Location: Institut Mittag-Leffler, Seminar Hall Kuskvillan and Zoom

Video link: Meeting ID: 921 756 1880

Participating: Danylo Radchenko (CNRS)

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As a part of asymptotic calculation of correlation functions in \(N=4\) supersymmetric Yang-Mills theory, Chester, Green, Pufu, Wang, and Wen have conjectured an unusual-looking weighted convolution identity involving the sum of squares of divisors function \(\sigma_2\). I will talk about a proof of this conjecture as well as a more general class of similar identities, which turn out to involve Fourier coefficients of cusp forms for \(\mathrm{SL}_2(\mathbb{Z})\). The talk is based on a recent joint work with Ksenia Fedosova and Kim Klinger-Logan.